How to fake fluid in a jar while moving jar around
You can use a Surface Deform Modifier on a higher poly mesh and run a cloth sim on a low poly mesh to make it look like water, OR just use the lower poly mesh, if you don't need realism:

High poly mesh --> Add cube --> subsurf modifier level 2 and apply it--> cut the bottom half off and delete in edit mode (so you have a half sphere) --> right click in edit mode and subdivide it 2 times --> Scale on z axis until flat-ish, like top of water 

Low poly mesh --> Add second cube --> subsurf modifier level 2 and apply it -> cut off bottom half again -->  Do Not subdivide more --> scale in edit mode so it's flat-ish, same shape or as close as you can get to the higher poly mesh --> align lower poly right on top of higher poly,very close

--> set surface deform modifier on high poly mesh, with low poly mesh as target -->  click bind 

--> set a cloth physics simulation on low poly mesh --> make outer ring of LP mesh a vertex group with weight of 1.000 --> use that vertex group as pinning group in cloth sim>Shape>Pin group (so it doesn't go flying off the screen, lol)--> adjust weight of cloth to .8 kg; Field Weights>Gravity to .001
EDIT: try switching "angular" to "linear" in ClothSim > Physical Properties > Bending Model.  This might smooth out the physics.

--> Add empty --> add force field>Vortex to empty --> set vortex strength to 200  

This should be a start, just play with the cloth simulation a little bit.
If you use higher poly, set lower poly to Not Render.

I'll come back and see if I can edit this later and maybe add a "How to" video, too tired right now.